Unplug the light. If the light is mounted to the wall or ceiling, turn off the power at the fuse box.
Tear off a 2-foot piece of duct tape.
Wrap the duct tape into a loop with the sticky side facing the inside. Be careful not to allow the rest of the tape to stick to itself.
Stick the center of the loop to the light bulb and flatten the ends to serve as handles.
Twist the handles, which will provide extra leverage to unscrew the light bulb. If the bulb breaks while you are unscrewing it, proceed to the next step.
Melt the spout of a water bottle with a lighter.
Press the water bottle's spout into the broken socket and let the plastic harden, fusing to the socket.
Use the water bottle as a handle to unscrew the socket.